On the Explanatory Role of Mathematics in Empirical Science

This paper examines contemporary attempts to explicate the explanatory role of mathematics in the physical sciences. Most such approaches involve developing so-called mapping accounts of the relationships between the physical world and mathematical structures. The paper argues that the use of idealizations in physical theorizing poses serious difficulties for such mapping accounts. A new approach to the applicability of mathematics is proposed. Introduction Mathematical Explanations I: Entities Mathematical Explanations II: Operations Mapping Accounts: Strengths Mapping Accounts: Idealizations 5.1Pincock and matching models 5.2Bueno, Colyvan, and the inferential conception Mapping Accounts: Limitations Suggestions for a New Approach Conclusion